Question

In the following exercises, solve each equation.

$e^{4x}.e^7=e^{19}$.

Short answer

The solution of the equation is$3$.

Step-by-step solution

Step 1. Given information.

The given equation is,

$e^{4x}.e^7=e^{19}$.

Step 2. Solving the equation.

Now to solve the equation we will write the same base on both sides of the equation and solve the obtained equation.

$$\begin{gathered} e^{4x}.e^7=e^{19} \\ {e}^{4x+7}=e^{19} \\ 4x+7=19 \\ 4x=12 \\ x=3 \end{gathered}$$

Step 3. Checking the result.

$$\begin{gathered} e^{4\left(3\right)}.e^7=e^{19} \\ {e}^{4\left(3\right)+7}=e^{19} \\ {e}^{12+7}=e^{19} \\ {e}^{19}=e^{19} \end{gathered}$$

Therefore, this is true.